Frameworks that create synergies across disciplines provide a powerful means for learning by relating concepts from the different fields that are usually difficult to grasp individually. We discuss the design of the BeatTable, a microworld that uses the relation between mathematics and music to engage learners in using ratios and proportions to create rhythms and learn about musical composition. The BeatTable is a physical table with a digital environment that can be controlled by tangible

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... uments, and through immediate auditory and visual feedback makes salient the relationships between math and music. With a low-floor, high-ceiling design philosophy, BeatTable provides learners the opportunity to build on their conceptions about music and to practice and hone their use of ratios and proportions. We present what our design choices, the technology used, and a description of initial user feedback. This also builds on previous work on rethinking the encoding of the knowledge and the representational infrastructure in the areas of mathematics, science [15] , and music.